Nine is a very strange number

Nine is a strange number. You may be aware that dividing 1 by 9 gives an interesting decimal, 0.11111111... You may even be aware that dividing 1 by 99 gives the equally interesting 0.0101010101... , and dividing 1 by 999 gives 0.001001001001... , etc.
But did you know that dividing 1 by the squares of these numbers gives even stranger results?
1 divided by 81 (9 squared) gives 0.012345679012345679... , i.e. consecutive digits, but with the 8 mysteriously missing. 1 divided by 9,801 (which is 99 squared) gives 0.000102030405060708091011121314... , which seems to generate all the two digit numbers in consecutive sequence (including 8). But, guess what? 98 is missing in the sequence. One step further, 1 divided by 998,001 (yes, that's 999 squared) gives 0.000001002003004005006... , all the 3 digit numbers in sequence. But - you guessed it again - one number is missing from the sequence: 998. And, yes, the same kind of thing happens with 99,980,001 (the square of 9,999), etc, etc.
I'm sure if the ancient Greeks or Hebrews had figured this out, they would have ascribed all sorts of spiritual and supernatural significance to these findings. Me, I just find it kind of quirky and interesting.